Probability of spin-orbit torque driven magnetization switching assisted by spin-transfer torque

Spin-orbit torque (SOT) driven magnetization switching, assisted by spin-transfer torque (STT), enables field-free switching in ferromagnetic nanostructures and is expected to be a writing method for next-generation spintronic nonvolatile memory. The role of STT is to shift the magnetization pointing in an in-plane direction via the SOT to a different direction and ensure the switching. Here, we study the dependence of the switching probability on the STT strength using a numerical simulation of the Landau-Lifshitz-Gilbert (LLG) equation. While a monotonic increase of the switching probability with increasing STT strength is found in a relatively weak STT region, we find an unexpected increase in the error rate in a relatively large STT current close to a critical current. Based on the statistical analysis of the magnetization dynamics and solving the LLG equation analytically, we reveal that the origin of the switching error is the presence of an inactive region in the Bloch sphere where the magnetization dynamics becomes very slow compared with conventional SOT switching. Since this region exists far away from the initial state of the magnetization, a strong STT is necessary to reach the region. Accordingly, the switching error increases in a strong STT region. We also show that the issue can be solved by reducing the time only the STT is applied and/or enhancing the SOT strength.